ASYMPTOTIC BEHAVIOR OF (a, k)-REGULARIZED RESOLVENT FAMILIES AT ZERO

Abstract

This paper is primarily concerned with approximation at 0 of an (a, k)-regularized resolvent family R(·) for Volterra integral equation. We shall consider convergence rates of some kind of local means Qm(t), t ≥ 0,m ≥ 0, of R(t)/k(t). Some approximation theorems and local ergodic theorems with rates will be deduced from general approximation theorems for regularized approximation processes.